started college and havent been doing so good and well i have this test soon and im having trouble with some questions... (i appologize in advance i have to translate from spanish... so if something sounds funny well ask me)

1) Determine the dimensions of the rectangle with the greatest area which perimeter is 8.

2) If x, y > 0. prove that:

2/((1/x)+(1/y)) <= sqrt(xy) <= (x+y)/2

3) If a, b, c are positive real numbers and different of each other, demonstrate that:

(a + b + c) / 3 > ((ab + bc + ca)/3)^(1/2) > (abc)^(1/3)

March 25th 2007, 01:59 PM

Jhevon

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Quote:

Originally Posted by sacwchiri

started college and havent been doing so good and well i have this test soon and im having trouble with some questions... (i appologize in advance i have to translate from spanish... so if something sounds funny well ask me)

1) Determine the dimensions of the rectangle with the greatest area which perimeter is 8.

This is an optimization problem. See the diagram below

The Calculus way to do this problem.

we have P = 2x + 2y = 8 ............P is the perimeter
and we want the area A = xy to be a maximum